Question

the difference between sqares of two numbers is 120 the sqares of smsller is twice the greatet number find the numbers​

Answer 1

Step-by-step explanation:

Let the numbers be x and y (x > y)

According to the given condition, x2 – y2 = 120

(i) y² = 2x

(ii) Substituting y = 2x in equation (i),

we get x² – 2x = 120

∴ x² – 2x – 120 = 0

∴ x² – 12x + 10x – 120 = 0

∴ x(x – 12) + 10(x – 12) = 0

∴ (x – 12)(x + 10) = 0

By using the property, if the product of two numbers is zero, then at least one of them is zero,

we get ∴ x – 12 = 0 or x + 10 = 0

∴ x = 12 or x = -10 But x ≠ -10

as, y² = 2x = 2(-10) = -20

[Since, the square of number cannot be negative]

∴ x = 12 Smaller number = y² =2x

∴ y²= 2 × 12

∴ y² = 24

∴ y = ± √24[Taking square root of both sides]

∴ The smaller number is √24 and greater number is 12

or the smaller number is – √24 and greater number is 12